1. Field of the Invention
The present invention relates to a method for measuring polarization characteristics and a measurement apparatus.
2. Description of the Related Art
Up to now, image forming performance of an optical system has been evaluated by measuring a wavefront aberration or the polarization characteristics of an optical system and then using those results as the image forming performance of the optical system. However in recent years the increase in the numerical aperture (NA) of optical systems has resulted in a need for increasingly rigorous control of polarization characteristics due to their considerable effect on image formation in the image plane.
As a result, there is a need for a highly accurate measuring technique for polarization characteristics. For example, polarization distribution can be measured using a polarizer such as a crystal on the image plane or the exit of the illumination system.
In addition, a wafer coated with a resist can be used for measuring. More specifically, the wafer is exposed with a mask pattern, which varies sensitively to polarized light.
The evaluation method requires measurement of the resist image formed by developing the resist after exposure using a scanning electron microscope (SEM) or the like. Since the evaluation method requires steps including resist coating, developing, and measuring, considerable time and cost are involved in a single evaluation cycle.
In addition, there is a method for obtaining a polarization ratio by forming an aerial image of the mask pattern in a position corresponding to the image plane without performing an actual exposure operation and then directly measuring a light intensity distribution of the image (hereafter “aerial image measuring method”) using a measurement apparatus. An example of this method employs slits for cutting out an aerial image and measuring the light passing through the slits using a light receiving element as discussed, for example, in Japanese Patent Application Laid-Open No. 2007-281463).
A typical slit scan method, for example, uses a slit A540 formed in the light blocking film A51 as illustrated in FIG. 14. FIG. 15 is a schematic diagram illustrating a measuring sensor for a slit scan method on a sectional plane connecting A0 and B0 in FIG. 14.
For example, a line-and-space pattern (hereafter “L/S”) is illuminated to form an aerial image 41 having a periodic intensity distribution. The light in a portion of the aerial image 41 passes through the slit A540, which has a width of substantially 3/2 times the period of the aerial image 41, and after passing through a transparent base plate A52 supporting a light blocking film A51, the light enters the light receiving element A53. The light incident upon the light receiving element A53 undergoes photoelectric conversion and is output as a slit signal S.
A measuring sensor A50 includes the light shielding film A51, the transparent base plate A52, and the light receiving element A53. The measuring sensor A50 is moved by a stage A60 in a stepwise manner by a step corresponding to half of the pitch of the L/S with respect to the x direction. The sensor A50 calculates a contrast by using sensor outputs that are output before and after the step movement respectively. The contrast expresses the level of tone as a ratio or difference between a maximum value and a minimum value of the light intensity and, for example, may be given by ((p−q)/(p+q) where a maximum value for light intensity is denoted as p and a minimum value as q.
The aerial image 41 varies in response to the ratio of polarization and the contrast gradually decreases as the p polarization component increases which results, for example, in a low-contrast light intensity distribution such as the aerial image 42. In other words, since the contrast fluctuates according to change in the ratio of polarization, the ratio of polarization can be calculated from the measured contrast if the relationship between the ratio of polarization and contrast is clearly identified.
There is a method of using two slits having different slit widths to measure an intensity ITE and ITM on an image plane of transverse electric (TE) polarized light and transverse magnetic (TM) polarized light as discussed, for example, in Japanese Patent Application Laid-Open No. 08-22953).
The transmissivity of TE polarized light in a slit 1 is denoted as ε1TE, the transmissivity of TM polarized light in a slit 1 is denoted as ε1TM, the transmissivity of TE polarized light in a slit 2 is denoted as ε2TE, and the transmissivity of TM polarized light in a slit 2 is denoted as ε2TM. Thus a light intensity I1(x) for an image plane obtained by scanning a slit 1 and a light intensity I2(x) for an image plane obtained by scanning a slit 2 is expressed in Equation (1).I1(x)=ε1TE·ITE+ε1TM·ITM I2(x)=ε2TE·ITE+ε2TM·ITM  (1)Solving the simultaneous equations for ITE and ITM obtains a light intensity ITE for the image plane of TE polarized light and a light intensity ITM for the image plane of TM polarized light.
However in the method of measuring contrast as discussed in Japanese Patent Application Laid-Open No. 2007-281463, the contrast change corresponding to change in the ratio of polarization displays low sensitivity. Furthermore in the absence of accurate control of the slit position, the contrast sometimes does not display a one to one relationship with the ratio of polarization, which therefore complicates the calculation of change in the ratio of polarization using contrast change.
FIG. 16 illustrates a relationship of contrast and the ratio of polarization obtained by simulation. A light source having a wavelength of 193 nm was used and water was introduced between the final plane and the image plane of the optical system. A light intensity distribution was formed on the image plane having a periodic contrast of 1 and a half pitch of 45 nm. The slits were formed in the light shielding film made of tantalum with a thickness of 150 nm. A ratio of polarization RoP is defined as Is/(Is+Ip). Is denotes the light intensity of sigma (s) polarized light and Ip is the light intensity of pi (p) polarized light.
When a slit width is 80 nm, even when RoP is varied from 1 to 0.9, the contrast only displays a 2% change. Furthermore, when the slit width is 160 nm, since there are two corresponding RoP values at a contrast of 0.5 or less, it is not possible to determine which of the two RoP values applies only with reference to the contrast.
As discussed in Japanese Patent Application Laid-Open No. 08-22953, a method for calculating an image plane intensity for each polarization direction by scanning two slits cannot be applied to a case where an aerial image and the intensity distribution of the measured image plane changes non-linearly.
For example, as illustrated in FIG. 17, when the intensity of the aerial image is denoted as Int0(x), a light intensity distribution S1(x) can be measured by one slit as a prescribed multiple of the aerial image. Using a constant a, it is expressed in Equation (2) as follows:S1(x)=a×Int0(x)  (2)
However when using the other slit to measure a light intensity distribution having a phase deviation from the aerial image such as S2(x), a prescribed multiple of the aerial image is not obtained and it is not possible to express S2(x) in the form of Equation (2). Consequently, it is sometimes the case that Equation (1) cannot be solved or that there is not a unique solution.